Abstract
In this paper, we propose an HBV viral infection model with continuous age structure and nonlinear incidence rate. Asymptotic smoothness of the semi-flow generated by the model is studied. Then we caculate the basic reproduction number and prove that it is a sharp threshold determining whether the infection dies out or not. We give a rigorous mathematical analysis on uniform persistence by reformulating the system as a system of Volterra integral equations. The global dynamics of the model is established by using suitable Lyapunov functionals and LaSalle's invariance principle. We further investigate the global behaviors of the HBV viral infection model with saturation incidence through numerical simulations.
Highlights
Over the past few years, within-host virus models have been studied extensively to describe the dynamics inside the host of various infectious diseases such as HIV, HBV and so on
Several within-host virus dynamics models have been constructed to investigate the dynamics of models to take saturation incidence rate or other nonlinear incidence rate into consideration [2, 6, 7, 9, 19, 21,22,23,24,25, 28, 29]
To analyze the global dynamics of system (3), it is necessary to prove the smoothness of the semi-flow generated by system (3)
Summary
Over the past few years, within-host virus models have been studied extensively to describe the dynamics inside the host of various infectious diseases such as HIV, HBV and so on. There exist less age-structured virus models to take both virus-to-cell and cell-to-cell infection into consideration. There is no certain observation suggesting that viruses infect cells with linear incidence rate Motivated by this fact, several within-host virus dynamics models have been constructed to investigate the dynamics of models to take saturation incidence rate or other nonlinear incidence rate into consideration [2, 6, 7, 9, 19, 21,22,23,24,25, 28, 29]. The function β2(a) ∈ L∞ + (0, ∞) is the infection-age specific transmission rate of reproductively infected cells, which is Lipschitz continuous and has a finite essential upper bound. P(a) is the viral production rate of an infected cell with age a. More details concerning the global stability analysis of virus models, we refer readers to [5,6,7, 9, 14, 18,19,20,21,22,23,24,25, 28, 29]
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